A-Level A-Level Mathematics 2

Question 1

What is the equation of a circle with centre (3, −2) and radius 5?

Accepted Answer

(x − 3)² + (y + 2)² = 25

Answer

The equation of a circle with centre (a, b) and radius r is (x − a)² + (y − b)² = r². With centre (3, −2) and radius 5: (x − 3)² + (y − (−2))² = 5², giving (x − 3)² + (y + 2)² = 25.

Question 2

What does it mean for a function to be 'continuous' at a point?

Accepted Answer

The limit of the function at that point exists, equals the function value, and there are no breaks or jumps

Answer

A function is continuous at point x = a if: (1) f(a) is defined, (2) the limit as x → a exists, and (3) the limit equals f(a). Informally, you can draw the curve without lifting your pen.

Question 3

What is the quotient rule for differentiation?

Accepted Answer

d/dx(u/v) = (u'v − uv')/v²

Answer

The quotient rule states: if y = u/v, then dy/dx = (u'v − uv')/v². Remember the order: differentiate the top times the bottom minus the top times the derivative of the bottom, all over the bottom squared.

Question 4

What does 'proof by contradiction' involve?

Accepted Answer

Assuming the statement is false and showing this leads to an impossibility

Answer

Proof by contradiction assumes the negation of the statement is true, then derives a logical contradiction. Since the assumption leads to an impossibility, the original statement must be true.

Question 5

What is the normal distribution and when is it used?

Accepted Answer

A symmetric, bell-shaped probability distribution described by mean (μ) and standard deviation (σ), used to model many natural phenomena

Answer

The normal distribution N(μ, σ²) is a continuous, symmetric, bell-shaped distribution. It models many real-world phenomena (heights, IQ, measurement errors). About 68% of values lie within 1σ of the mean; 95% within 2σ.

A-Level Revision Practice Test

A-Level Revision Practice Test

A-Level A-Level Mathematics 2